There is another way to attach an integer to each primary decoration
in M besides the period. In Figure 8 we have displayed the
filled Julia set
for c = -0.12 + 0.75i. This filled Julia set is often called Douady's
rabbit. Note that the image looks like a "fractal rabbit." The
rabbit has a main body with two ears attached. But everywhere you look
you see other pairs of ears.

Figure 8. The fractal rabbit

Another way to say this is that the filled Julia set contains infinitely many
"junction points" at which 3 distinct black regions in Jc are
attached. In Figure 9 we have magnified a portion of the fractal
rabbit to illustrate this.

Figure 9. A magnification of the fractal rabbit

The fact that each junction point in this filled Julia set has 3 pieces
attached is no surprise, since this c-value lies in a primary period
3 bulb in the Mandelbrot set. This is another fascinating fact about
M. If you choose a c-value from one of the primary
decorations in M, then, first of all, Jc must be a
connected set, and second, Jc contains infinitely many special
junction points and each of these points has exactly n regions
attached to it, where n is exactly the period of the bulb.
Figure 10 illustrates this for periods 4 and 5.